Clear visibility and $L_ 2$ sets
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- by N. Stavrakas PDF
- Proc. Amer. Math. Soc. 103 (1988), 1213-1215 Request permission
Abstract:
Let $S \subset {R^2}$ be a closed connected set whose points of local nonconvexity are compact. Suppose any two points of local nonconvexity are clearly visible from a common point of $S$. Then $S$ is almost starshaped and $S$ is $2$-polygonally connected. This generalizes a result of Breen.References
- Marilyn Breen, Clear visibility and sets which are almost starshaped, Proc. Amer. Math. Soc. 91 (1984), no. 4, 607–610. MR 746099, DOI 10.1090/S0002-9939-1984-0746099-5
- Alfred Horn and F. A. Valentine, Some properties of $L$-sets in the plane, Duke Math. J. 16 (1949), 131–140. MR 28582
- F. A. Valentine, Local convexity and $L_{n}$ sets, Proc. Amer. Math. Soc. 16 (1965), 1305–1310. MR 185510, DOI 10.1090/S0002-9939-1965-0185510-6
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 1213-1215
- MSC: Primary 52A30; Secondary 52A35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0955012-0
- MathSciNet review: 955012